Generalized Absolute Mean Strong Ergodicity For Nonhomogeneous Markov Chains

The aim of this work is to create some theorems about generalized absolute mean strong ergodicity for the countable nonhomogeneous Markov chains.Firstly,we define absolute mean strong ergodicity and generalized absolute mean strong ergodicity for countable nonhomogeneous Markov chain.Then,we prove main theorem regarding generalized absolute mean strong ergodicity for countable nonhomogeneous Markov chain and give some applications.We also propose a simple proof of equivalence of weak and strong ergodicity for homogeneous Markov chain.